Systems, apparatuses and methods for delivery of ablative energy to tissue

ABSTRACT

A system includes a pulse waveform generator and an ablation device coupled to the pulse waveform generator. The ablation device includes at least one electrode configured for ablation pulse delivery to tissue during use. The pulse waveform generator is configured to deliver voltage pulses to the ablation device in the form of a pulsed waveform. A first level of a hierarchy of the pulsed waveform includes a first set of pulses, each pulse having a pulse time duration, with a first time interval separating successive pulses. A second level of the hierarchy of the pulsed waveform includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses, the second time interval being at least three times the duration of the first time interval.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 16/416,677, titled “SYSTEMS, APPARATUSES AND METHODS FOR DELIVERY OF ABLATIVE ENERGY TO TISSUE”, filed May 20, 2019, now issued as U.S. Pat. No. 10,512,779, which is a continuation of U.S. patent application Ser. No. 15/796,375 titled “SYSTEMS, APPARATUSES AND METHODS FOR DELIVERY OF ABLATIVE ENERGY TO TISSUE”, filed Oct. 27, 2017, now issued as U.S. Pat. No. 10,322,286, which is a continuation of U.S. patent application Ser. No. 15/334,646 titled “SYSTEMS, APPARATUSES AND METHODS FOR DELIVERY OF ABLATIVE ENERGY TO TISSUE”, filed Oct. 26, 2016, now abandoned, which is a continuation of PCT Application No. PCT/US2016/057664 titled “SYSTEMS, APPARATUSES AND METHODS FOR DELIVERY OF ABLATIVE ENERGY TO TISSUE”, filed Oct. 19, 2016, which claims priority to U.S. Provisional Application Ser. No. 62/274,926 titled “METHOD AND APPARATUS FOR DELIVERY OF PULSED ELECTRIC FIELD ABLATIVE ENERGY TO TISSUE”, filed Jan. 5, 2016, the entire disclosures of which are incorporated herein by reference in their entirety.

BACKGROUND

The generation of pulsed electric fields for tissue therapeutics has moved from the laboratory to clinical applications over the past two decades, while the effects of brief pulses of high voltages and large electric fields on tissue have been investigated for the past forty years or more. Application of brief high DC voltages to tissue, which can generate locally high electric fields typically in the range of hundreds of Volts/centimeter, can disrupt cell membranes by generating pores in the cell membrane. While the precise mechanism of this electrically-driven pore generation or electroporation is unclear, it is thought that the application of relatively large electric fields generates instabilities in the lipid bilayers in cell membranes, causing the occurrence of a distribution of local gaps or pores in the membrane. If the applied electric field at the membrane is larger than a threshold value, the electroporation can be irreversible and the pores remain open, permitting exchange of biomolecular material across the membrane and leading to necrosis and/or apoptosis (cell death). Subsequently the surrounding tissue heals in a natural process.

Hence, known electroporation applications in medicine and delivery methods do not address high voltage application, tissue selectivity, and safe energy delivery, especially in the context of ablation therapy for cardiac arrhythmias with catheter devices. Further, there is an unmet need for thin, flexible, atraumatic devices that can at the same time effectively deliver high DC voltage electroporation ablation therapy selectively to tissue in regions of interest while minimizing damage to healthy tissue, and for a combination of device design and dosing waveform that involves minimal or no device repositioning, permitting an effective, safe and rapid clinical procedure.

SUMMARY

A system includes a pulse waveform generator and an ablation device coupled to the pulse waveform generator. The ablation device includes at least one electrode configured for ablation pulse delivery to tissue during use. The pulse waveform generator is configured to deliver voltage pulses to the ablation device in the form of a pulsed waveform. A first level of a hierarchy of the pulsed waveform includes a first set of pulses, each pulse having a pulse time duration, with a first time interval separating successive pulses. A second level of the hierarchy of the pulsed waveform includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses, the second time interval being at least three times the duration of the first time interval.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic illustration of a catheter with a plurality of electrodes disposed along its distal shaft, epicardially disposed such that it snugly wraps around the pulmonary veins of a cardiac anatomy, according to embodiments.

FIG. 2 is an example waveform showing a sequence of voltage pulses with a pulse width defined for each pulse, according to embodiments.

FIG. 3 schematically illustrates a hierarchy of pulses showing pulse widths, intervals between pulses, and groupings of pulses, according to embodiments.

FIG. 4 provides a schematic illustration of a nested hierarchy of monophasic pulses displaying different levels of nested hierarchy, according to embodiments.

FIG. 5 is a schematic illustration of a nested hierarchy of biphasic pulses displaying different levels of nested hierarchy, according to embodiments.

FIG. 6 schematically shows a circle of numbered catheter electrodes, wherein sets of electrodes can be sequentially selected for application of a corresponding sequence of voltage pulse waveforms, according to embodiments.

FIG. 7 illustrates schematically a time sequence of electrocardiograms and cardiac pacing signals together with atrial and ventricular refractory time periods and indicating a time window for irreversible electroporation ablation, according to embodiments.

FIG. 8 illustrates schematically a time sequence of electrode set activations delivered as a series of waveform packets over a corresponding series of successive heartbeats, according to embodiments.

FIG. 9 is a schematic illustration of an irreversible electroporation system that includes a system console that in turn includes a voltage/signal generator, a controller configured to apply voltages to selected subsets of electrodes and that is communicably connected to a computer or processor together with a user interface, and a switching unit configured to electrically isolate other equipment from voltage pulses that may be delivered to an ablation catheter from the voltage generator, according to embodiments.

FIG. 10 is a schematic illustration of a user interface in an initial configuration, according to embodiments.

FIG. 11 is a schematic illustration of a user interface showing the engagement of an initialization function, according to embodiments.

FIG. 12 is a schematic illustration of a user interface showing a required step subsequent to initialization, according to embodiments.

FIG. 13 is a schematic illustration of a user interface showing a configuration where the system is ready, subsequent to the completion of a prior step, for delivery of ablative energy. In this configuration the user interface includes a button for ablation, according to embodiments.

DETAILED DESCRIPTION

The terms “about” and “approximately” as used herein in connection with a referenced numeric indication means the referenced numeric indication plus or minus up to 10% of that referenced numeric indication. For example, the language “about 50” units or “approximately 50” units means from 45 units to 55 units.

In some embodiments, a system includes a pulse waveform generator and an ablation device coupled to the pulse waveform generator. The ablation device includes at least one electrode configured for ablation pulse delivery to tissue during use. The pulse waveform generator is configured to deliver voltage pulses to the ablation device in the form of a pulsed waveform. A first level of a hierarchy of the pulsed waveform includes a first set of pulses, each pulse having a pulse time duration, a first time interval separating successive pulses. A second level of the hierarchy of the pulsed waveform includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses, the second time interval being at least three times the duration of the first time interval. A third level of the hierarchy of the pulsed waveform includes a plurality of second sets of pulses as a third set of pulses, a third time interval separating successive second sets of pulses, the third time interval being at least 30 times the duration of the second time interval.

In some embodiments, the pulses of each first set of pulses include monophasic pulses with a voltage amplitude of at least 800 Volts. In some embodiments, the pulse time duration of each monophasic pulse is in the range from about 1 microsecond to about 300 microseconds.

In some embodiments, the pulses of each first set of pulses include biphasic pulses each with a voltage amplitude of at least 800 Volts. In some embodiments, the pulse time duration of each biphasic pulse is in the range from about 0.5 nanosecond to about 20 microseconds.

In some embodiments, each second set of pulses includes at least 2 first sets of pulses and less than 40 first sets of pulses. In some embodiments, each third set of pulses includes at least 2 second sets of pulses and less than 30 second sets of pulses. In some embodiments, the second time interval is at least ten times the pulse time duration.

In some embodiments, the ablation device includes an ablation catheter configured for epicardial placement. In some embodiments, the ablation device includes an ablation catheter configured for endocardial placement.

In some embodiments, a system includes a pulse waveform generator, and an ablation device coupled to the pulse waveform generator, the ablation device including at least one electrode configured for ablation pulse delivery to tissue during use. The pulse waveform generator is configured to deliver voltage pulses to the ablation device in the form of a pulsed waveform. A first level of a hierarchy of the pulsed waveform includes a first set of pulses, each pulse having a pulse time duration, a first time interval separating successive pulses. A second level of the hierarchy of the pulsed waveform includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first set of pulses. In some embodiments, the second time interval is at least three times the duration of the first time interval. A third level of the hierarchy of the pulsed waveform includes a plurality of second sets of pulses as a third set of pulses, a third time interval separating successive second sets of pulses. In some embodiments, the third time interval is at least thirty times the duration of the second time interval. The pulse waveform generator is configured to apply a plurality of the third sets of pulses to the ablation device with a time delay of at most about 5 milliseconds between successive third sets of pulses applied over different electrode sets.

In some embodiments, the ablation device includes an ablation catheter configured for epicardial placement. In some embodiments, the ablation catheter includes at least four electrodes.

In some embodiments, each second set of pulses includes at least 2 first sets of pulses and less than 40 first sets of pulses. In some embodiments, each third set of pulses includes at least 2 second sets of pulses and less than 30 second sets of pulses. In some embodiments, the pulses of each first set of pulses has a voltage amplitude of at least 800 Volts.

In some embodiments, a system includes a pulse waveform generator and an ablation device coupled to the pulse waveform generator, the ablation device including at least one electrode configured for ablation pulse delivery to tissue during use. The system also includes a cardiac stimulator coupled to the pulse waveform generator, the cardiac stimulator configured for generating pacing signals for cardiac stimulation during use. The pulse waveform generator is configured to deliver voltage pulses to the ablation device in the form of a pulsed waveform, the pulsed waveform being in synchrony with the pacing signals. A first level of a hierarchy of the pulsed waveform includes a first set of pulses, each pulse having a pulse time duration, a first time interval separating successive pulses. A second level of the hierarchy of the pulsed waveform includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses. A third level of the hierarchy of the pulsed waveform includes a plurality of second sets of pulses as a third set of pulses, a third time interval separating successive second sets of pulses. The pulse waveform generator is configured to generate the pulsed waveform such that each of the first sets of pulses and each of the second sets of pulses, the plurality of second sets of pulses, the predetermined number of electrode sets, the time delay, the pulse time duration, the first time interval, the second time interval, and the third time interval are jointly constrained by a Diophantine inequality.

In some embodiments, the Diophantine inequality constraint is further characterized by a refractory time window. In some embodiments, a number of the first sets of pulses and a number of the second sets of pulses are pre-determined.

In some embodiments, the pulse waveform generator is further configured to deliver the pulsed waveform spaced from the pacing signals by a time offset, the time offset being smaller than about 25 milliseconds. In some embodiments, the third time interval corresponds to a pacing period associated with the pacing signals. In some embodiments, the second time interval is at least three times the duration of the first time interval. In some embodiments, the third time interval is at least thirty times the duration of the second time interval. In some embodiments, the second level time interval is at least ten times the duration of the pulse time duration.

In some embodiments, the ablation device includes an ablation catheter configured for epicardial placement. In some embodiments, the ablation device includes an ablation catheter configured for endocardial placement.

In some embodiments, a system includes a pulse waveform generator including a user interface and an ablation device coupled to the pulse waveform generator, the ablation device including a plurality of electrodes configured for ablation pulse delivery to tissue of a patient during use. The system also includes a cardiac stimulator coupled to the pulse waveform generator, the cardiac stimulator configured for generating pacing signals for cardiac stimulation of the patient during use. The pulse waveform generator is configured to deliver voltage pulses to the ablation device in the form of a pulsed voltage waveform having at least three levels of hierarchy. The pulse waveform generator is further configured to deliver the pulsed voltage waveform in synchrony with the pacing signals, and to deliver the pulsed voltage waveform upon receipt of the indication of user confirmation.

In some embodiments, a first level of a hierarchy of the pulsed waveform includes a first set of pulses, each pulse having a pulse time duration, a first time interval separating successive pulses. In some embodiments, a second level of the hierarchy of the pulsed waveform includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses. In some embodiments, a third level of the hierarchy of the pulsed waveform includes a plurality of second sets of pulses as a third set of pulses, a third time interval separating successive second sets of pulses. In some embodiments, the pulse waveform generator is further configured to apply a plurality of third sets of pulses to a predetermined number of electrode sets of the ablation device with a time delay between successive third sets of pulses. In some embodiments, each of the first sets of pulses and each of the second sets of pulses, the predetermined number of electrode sets, the time delay, the pulse time duration, the first time interval, the second time interval, and the third time interval are jointly constrained by a Diophantine inequality.

In some embodiments, the pulse waveform generator is configured to deliver the pulsed waveform only after a pre-determined time interval after the indication of user confirmation. In some embodiments, the user interface includes a control input device, and the pulse waveform generator is configured to deliver the pulsed waveform upon user engagement of the control input device.

In some embodiments, a method includes generating a pulsed waveform. The pulsed waveform includes a first level of a hierarchy of the pulsed waveform that includes a first set of pulses, each pulse having a pulse time duration, a first time interval separating successive pulses. The pulse waveform also includes a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses, the second time interval being at least three times the duration of the first time interval. The pulse waveform a third level of the hierarchy of the pulsed waveform includes a plurality of second sets of pulses as a third set of pulses, a third time interval separating successive second sets of pulses, the third time interval being at least thirty times the duration of the second level time interval. The method also includes delivering the pulsed waveform to an ablation device.

In some embodiments, a method includes generating a pulsed waveform. The pulsed waveform includes a first level of a hierarchy of the pulsed waveform that includes a first set of pulses, each pulse having a pulse time duration, a first time interval separating successive pulses. The pulsed waveform also includes a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses, a second time interval separating successive first sets of pulses, the second time interval being at least three times the duration of the first time interval. The pulsed waveform also includes a third level of the hierarchy of the pulsed waveform includes a plurality of second sets of pulses as a third set of pulses, a third time interval separating successive second sets of pulses, the third time interval being at least thirty times the duration of the second level time interval. The method also includes generating pacing signals with a cardiac stimulator. The method also includes delivering, in synchrony with the pacing signals, the pulsed waveform to an ablation device.

Disclosed herein are methods, systems and apparatuses for the selective and rapid application of pulsed electric fields/waveforms to effect tissue ablation with irreversible electroporation. Some embodiments are directed to pulsed high voltage waveforms together with a sequenced delivery scheme for delivering energy to tissue via sets of electrodes. In some embodiments, the electrodes are catheter-based electrodes, or a plurality of electrodes disposed along the length of an elongate medical device. In some embodiments, a system useful for irreversible electroporation includes a voltage/signal generator and a controller capable of being configured to apply pulsed voltage waveforms to a selected plurality or a subset of electrodes of an ablation device. In some embodiments, the controller is configured to control inputs whereby selected pairs of anode-cathode subsets of electrodes can be sequentially triggered based on a pre-determined sequence, and in one embodiment the sequenced delivery can be triggered from a cardiac stimulator or pacing system/device. In some embodiments, the ablation pulse waveforms are applied in a refractory period of the cardiac cycle so as to avoid disruption in rhythm regularity of the heart. One example method of enforcing this is to electrically pace the heart with a cardiac stimulator and ensure pacing capture to establish periodicity and predictability of the cardiac cycle, and then to define a time window well within the refractory period of this periodic cycle within which the ablation waveform is delivered.

In some embodiments, the pulsed voltage waveforms disclosed herein are hierarchical in organization and have a nested structure. In some embodiments, the pulsed waveform includes hierarchical groupings of pulses with a variety of associated timescales. Furthermore, the associated timescales and pulse widths, and the numbers of pulses and hierarchical groupings, can be selected so as to satisfy one or more of a set of Diophantine inequalities involving the frequency of cardiac pacing.

Pulsed waveforms for electroporation energy delivery as disclosed herein can enhance the safety, efficiency and effectiveness of the energy delivery by reducing the electric field threshold associated with irreversible electroporation, yielding more effective ablative lesions with reduced total energy delivered. This in turn can broaden the areas of clinical application of electroporation including therapeutic treatment of a variety of cardiac arrhythmias.

The present disclosure addresses the need for devices and methods for rapid, selective and safe delivery of irreversible electroporation therapy, generally with multiple devices, such that, in some embodiments, peak electric field values can be reduced and/or minimized while at the same time sufficiently large electric field magnitudes can be maintained in regions where tissue ablation is desired. This also reduces the likelihood of excessive tissue damage or the generation of electrical arcing, and locally high temperature increases.

FIG. 1 is a schematic illustration of a catheter 15 with a plurality of electrodes disposed along its shaft. The catheter is shown in FIG. 1 in relation to a heart 7 and the catheter 15 is wrapped epicardially around the pulmonary veins of the left atrium denoted by reference characters 10, 11, 12 and 13 (respectively Left Superior, Left Inferior, Right Superior and Right Inferior in FIG. 1) and has electrodes indicated by dark bands (such as those denoted by reference character 17 in FIG. 1) that are wrapped and/or looped in a contour around the pulmonary veins 10, 11, 12, 13 of the left atrium. In some embodiment, catheter ends 8 and 9 are tightly drawn together and held inside a cinching tool (not shown) in order to ensure that the catheter electrodes are snugly wrapped around the pulmonary veins 10, 11, 12, 13. A method and apparatus using a subxiphoid pericardial access location and a guidewire-based delivery method to accomplish the placement of a multi-electrode ablation catheter around the pulmonary veins was described in PCT Patent Application Publication No. WO2014/025394, entitled “Catheters, Catheter Systems and Methods for Puncturing Through a Tissue Structure and Ablating a Tissue Region”, the entire disclosure of which are incorporated herein by reference in its entirety.

In some embodiments, the catheter electrodes 17 can be constructed in the form of metallic bands or rings. In some embodiments, each electrode 17 can be constructed so as to be flexible. For example, the electrodes 17 can be in the form of metallic coiled springs or helical windings around the shaft of the catheter 15. As another example, the electrode(s) 17 can be in the form of a series of metallic bands or rings disposed along the shaft and that are electrically connected together, with the flexible portions of catheter shaft between the electrodes providing flexibility to the entire electrode. In some embodiments, at least a portion of the electrodes 17 can include biocompatible metals such as, but not limited to, titanium, palladium, silver, platinum and/or platinum alloys. In some embodiments, at least a portion of the electrodes 17 includes platinum and/or platinum alloys. In some embodiments, the catheter shaft can be made of a flexible polymeric material such as (for purposes of non-limiting examples only) polytetrafluorethylene, polyamides such as nylon, or polyether block amide. The electrodes 17 can be connected to insulated electrical leads (not shown) leading to a proximal handle portion of the catheter 15 (not shown), with the insulation on each of the leads being capable of sustaining an electrical potential difference of at least 700V across its thickness without dielectric breakdown. While the catheter 15 is placed epicardially as shown in FIG. 1, i.e. beneath the pericardium, in alternate embodiments the ablation catheter can be additionally or alternatively useful for endocardial placement.

FIG. 2 illustrates a pulsed voltage waveform in the form of a sequence of rectangular double pulses, with each pulse, such as the pulse 101 being associated with a pulse width or duration. The pulse width/duration can be about 0.5 microseconds, about 1 microsecond, about 5 microseconds, about 10 microseconds, about 25 microseconds, about 50 microseconds, about 100 microseconds, about 125 microseconds, about 140 microseconds, about 150 microseconds, including all values and sub-ranges in between. The pulsed waveform of FIG. 2 illustrates a set of monophasic pulses where the polarities of all the pulses are the same (all positive in FIG. 2, as measured from a zero baseline). In some embodiments, such as for irreversible electroporation applications, the height of each pulse 101 or the voltage amplitude of the pulse 101 can be about 400 Volts, about 1000 Volts, about 5000 Volts, about 10,000 Volts, about 15,000 Volts, including all values and sub ranges in between. As illustrated in FIG. 2, the pulse 101 is separated from a neighboring pulse by a time interval 102, also sometimes referred to as a first time interval. The first time interval can be about 10 microseconds, about 50 microsecond, about 100 microseconds, about 200 microseconds, about 500 microseconds, about 800 microseconds, about 1 millisecond including all values and sub ranges in between, in order to generate irreversible electroporation.

FIG. 3 introduces a pulse waveform with the structure of a hierarchy of nested pulses. FIG. 3 shows a series of monophasic pulses such as pulse 115 with pulse width/pulse time duration w, separated by a time interval (also sometimes referred to as a first time interval) such as 118 of duration t₁ between successive pulses, a number m₁ of which are arranged to form a group of pulses 121 (also sometimes referred to as a first set of pulses). Furthermore, the waveform has a number m₂ of such groups of pulses (also sometimes referred to as a second set of pulses) separated by a time interval 119 (also sometimes referred to as a second time interval) of duration t₂ between successive groups. The collection of m₂ such pulse groups, marked by 122 in FIG. 3, constitutes the next level of the hierarchy, which can be referred to as a packet and/or as a second set of pulses. The pulse width and the time interval t₁ between pulses can both be in the range of microseconds to hundreds of microseconds, including all values and sub ranges in between. In some embodiments, the time interval t₂ can be at least three times larger than the time interval t₁. In some embodiments, the ratio t₂/t₁ can be in the range between about 3 and about 300, including all values and sub-ranges in between.

FIG. 4 further elaborates the structure of a nested pulse hierarchy waveform. In this figure, a series of m₁ pulses (individual pulses not shown) form a group of pulses 130 (e.g., a first set of pulses). A series of m₂ such groups separated by an inter-group time interval 142 of duration t₂ (e.g., a second time interval) between one group and the next form a packet 132 (e.g., a second set of pulses). A series of m₃ such packets separated by time intervals 144 of duration t₃ (e.g., a third time interval) between one packet and the next form the next level in the hierarchy, a super-packet labeled 134 (e.g., a third set of pulses) in the figure. In some embodiments, the time interval t₃ can be at least about thirty times larger than the time interval t₂. In some embodiments, the time interval t₃ can be at least fifty times larger than the time interval t₂. In some embodiments, the ratio t₃/t₂ can be in the range between about 30 and about 800, including all values and sub-ranges in between. The amplitude of the individual voltage pulses in the pulse hierarchy can be anywhere in the range from 500 Volts to 7,000 Volts or higher, including all values and sub ranges in between.

FIG. 5 provides an example of a biphasic waveform sequence with a hierarchical structure. In the example shown in the figure, biphasic pulses such as 151 have a positive voltage portion as well as a negative voltage portion to complete one cycle of the pulse. There is a time delay 152 (e.g., a first time interval) between adjacent cycles of duration t₁, and n₁ such cycles form a group of pulses 153 (e.g., a first set of pulses). A series of n₂ such groups separated by an inter-group time interval 156 (e.g., a second time interval) of duration t₂ between one group and the next form a packet 158 (e.g., a second set of pulses). The figure also shows a second packet 162, with a time delay 160 (e.g., a third time interval) of duration t₃ between the packets. Just as for monophasic pulses, higher levels of the hierarchical structure can be formed as well. The amplitude of each pulse or the voltage amplitude of the biphasic pulse can be anywhere in the range from 500 Volts to 7,000 Volts or higher, including all values and sub ranges in between. The pulse width/pulse time duration can be in the range from nanoseconds or even sub-nanoseconds to tens of microseconds, while the delays t₁ can be in the range from zero to several microseconds. The inter-group time interval t₂ can be at least ten times larger than the pulse width. In some embodiments, the time interval t₃ can be at least about twenty times larger than the time interval t₂. In some embodiments, the time interval t₃ can be at least fifty times larger than the time interval t₂.

Embodiments disclosed herein include waveforms structured as hierarchical waveforms that include waveform elements/pulses at various levels of the hierarchy. The individual pulses such as 115 in FIG. 3 comprise the first level of the hierarchy, and have an associated pulse time duration and a first time interval between successive pulses. A set of pulses, or elements of the first level structure, form a second level of the hierarchy such as the group of pulses/second set of pulses 121 in FIG. 3. Among other parameters, associated with the waveform are parameters such as a total time duration of the second set of pulses (not shown), a total number of first level elements/first set of pulses, and second time intervals between successive first level elements that describe the second level structure/second set of pulses. In some embodiments, the total time duration of the second set of pulses can be between about 20 microseconds and about 10 milliseconds, including all values and sub-ranges in between. A set of groups, second set of pulses, or elements of the second level structure, form a third level of the hierarchy such as the packet of groups/third set of pulses 122 in FIG. 3. Among other parameters, there is a total time duration of the third set of pulses (not shown), a total number of second level elements/second set of pulses, and third time intervals between successive second level elements that describe the third level structure/third set of pulses. In some embodiments, the total time duration of the third set of pulses can be between about 60 microseconds and about 200 milliseconds, including all values and sub ranges in between. The generally iterative or nested structure of the waveforms can continue to a higher plurality of levels, such as ten levels of structure, or more.

In some embodiments, hierarchical waveforms with a nested structure and hierarchy of time intervals as described herein are useful for irreversible electroporation ablation energy delivery, providing a good degree of control and selectivity for applications in different tissue types. A variety of hierarchical waveforms can be generated with a suitable pulse generator. It is understood that while the examples herein identify separate monophasic and biphasic waveforms for clarity, it should be noted that combination waveforms, where some portions of the waveform hierarchy are monophasic while other portions are biphasic, can also be generated/implemented.

In embodiments directed to treatment of cardiac ablation, the pulse waveforms described above can be applied with electrode bipoles selected from a set of electrodes on a catheter, such as an ablation catheter. A subset of electrodes of the catheter can be chosen as anodes, while another subset of electrodes of the ablation catheter can be chosen as cathodes, with the voltage waveform being applied between anodes and cathodes. As a non-limiting example, in instances where the ablation catheter is an epicardially placed ablation catheter, the catheter can be wrapped around the pulmonary veins, and one electrode can be chosen as anode and another electrode can be chosen as cathode. FIG. 6 illustrates an example circular catheter configuration, where approximately diametrically opposite electrode pairs (e.g., electrodes 603 and 609, electrodes 604 and 610, electrodes 605 and 611, and electrodes 606 and 612) are activatable as anode-cathode sets. Any of the pulse waveforms disclosed can be progressively or sequentially applied over a sequence of such electrode sets. As a non-limiting example, FIG. 6 depicts a sequence of electrode subset activations. As a first step, electrodes 603 and 609 are selected as anode and cathode respectively, and a voltage waveform with a hierarchical structure described herein is applied across these electrodes. With a small time delay (e.g., less than about 5 milliseconds), as a next step electrodes 604 and 610 are selected as anode and cathode respectively, and the waveform is applied again across this set of electrodes. After a small time delay, as a next step electrodes 605 and 611 are selected as anode and cathode respectively for the next application of the voltage waveform. In the next step, after a small time delay, electrodes 606 and 612 are selected as anode and cathode respectively for voltage waveform application. In some embodiments, one or more of the waveforms applied across electrode pairs is applied during the refractory period of a cardiac cycle, as described in more detail herein.

In some embodiments, the ablation pulse waveforms described herein are applied during the refractory period of the cardiac cycle so as to avoid disruption of the sinus rhythm of the heart. In some embodiments, a method of treatment includes electrically pacing the heart with a cardiac stimulator to ensure pacing capture to establish periodicity and predictability of the cardiac cycle, and then defining a time window within the refractory period of the cardiac cycle within which one or more pulsed ablation waveforms can be delivered. FIG. 7 illustrates an example where both atrial and ventricular pacing is applied (for instance, with pacing leads or catheters situated in the right atrium and right ventricle respectively). With time represented on the horizontal axis, FIG. 7 illustrates a series of ventricular pacing signals such as 64 and 65, and a series of atrial pacing signals such as 62 and 63, along with a series of ECG waveforms 60 and 61 that are driven by the pacing signals. As indicated in FIG. 7 by the thick arrows, there is an atrial refractory time window 68 and a ventricular refractory time window 69 that respectively follow the atrial pacing signal 62 and the ventricular pacing signal 64. As shown in FIG. 7, a common refractory time window 66 of duration T_(r) can be defined that lies within both atrial and ventricular refractory time windows 68, 69. In some embodiments, the electroporation ablation waveform(s) can be applied in this common refractory time window 66. The start of this refractory time window 68 is offset from the pacing signal 64 by a time offset 59 as indicated in FIG. 7. The time offset 59 can be smaller than about 25 milliseconds, in some embodiments. At the next heartbeat, a similarly defined common refractory time window 67 is the next time window available for application of the ablation waveform(s). In this manner, the ablation waveform(s) may be applied over a series of heartbeats, at each heartbeat remaining within the common refractory time window. In one embodiment, each packet of pulses as defined above in the pulse waveform hierarchy can be applied over a heartbeat, so that a series of packets is applied over a series of heartbeats, for a given electrode set.

A timing sequence of electrode activation over a series of electrode sets is illustrated in FIG. 8, according to embodiments. Using the example scenario where it is desired to apply a hierarchical ablation waveform to j electrode sets (each electrode set comprising in general at least one anode and at least one cathode, in some embodiments, cardiac pacing is utilized as described in the foregoing, and a packet of pulses (such as including one or more pulse groups, or one or more sets of pulses) is applied first to electrode set 1, and with only a small time delay t_(d) (of the order of about 100 μs or less) this is followed by the packet of pulses being applied to electrode set 2. Subsequently, with another time delay, the packet of pulses is applied to electrode set 3, and so on to electrode set j. This sequence 632 of applications of the packet of pulses to all the j electrode sets is delivered during a single heartbeat's refractory time window (such as the common refractory time window 66 or 67), and each application to an electrode set constitutes one packet for that electrode set. Consider now the case of a monophasic hierarchical waveform. Referring to the monophasic waveform example shown in FIG. 3, the waveform has a series of monophasic pulses each with pulse width w, separated by a time interval of duration t₁ between successive pulses, a number m₁ of which are arranged to form a group of pulses. Furthermore, the waveform has a number m₂ of such groups of pulses separated by a time interval of duration t₂ between successive groups, thereby defining a packet. If this waveform is applied in sequence over the j electrode sets as described here, we can write the inequality j[m ₂(m ₁ w+t ₁(m ₁−1))+t ₂(m ₂−1)]+t _(d)(j−1)<T _(r)  (1) that the pulse waveform parameters m₁ and m₂ must satisfy for a given number of electrode sets j, in order for the entire ablation pulse delivery to occur within a refractory time window T_(r). In some embodiments, the refractory time window T_(r) can be about 140 milliseconds or less. The time offset of the start of the refractory window with respect to a pacing signal can be less than about 10 milliseconds. While the time intervals w, t₁, t₂ and t_(d) can be arbitrary, when implemented with finite state machines such as (for example) a computer processor, they are integers as measured in some suitable units (such as, for example, microseconds, nanoseconds or multiples of a fundamental processor clock time period). Given a number of electrode sets j, equation (1) represents a Diophantine inequality mutually constraining the pulse waveform parameters (pulse width, time intervals and numbers of pulses and groups) such that the total duration of the waveform application over the j electrode sets is smaller than a given common refractory period. In some embodiments, a solution set for the Diophantine inequality can be found based on partial constraints on the pulse waveform parameters. For example, the generator can require input of some of the pulse waveform parameters and/or related parameters, for example the pulse width w and time delay t_(d), after which the system console determines the rest of the pulse waveform parameters. In this case the number of electrode sets j is also an input to the system that constrains the solution determination. In one embodiment the system console could display more than one such possible solution set of waveform parameters for the user to make a selection, while in an alternate embodiment the system makes an automatic selection or determination of the waveform parameters. In some embodiments, a solution can be calculated and directly implemented in pre-determined form, such as, for example, on a pulse generator system console. For example, all of the pulse waveform parameters are pre-determined to satisfy a Diophantine inequality similar to equation (1) and the waveform is pre-programmed on the system; possibly the pre-determined solution(s) can depend on the number of electrode sets j, or alternately the solution(s) can be pre-determined assuming a maximal number for the electrode sets. In some embodiments more than one solution could be pre-determined and made available for user selection on the system console.

While the Diophantine inequality (1) holds for delivery of a single waveform packet over a single refractory time window, the full waveform can sometimes involve a plurality of packets. The number of packets can be pre-determined and in one embodiment can range from 1 to 28 packets, including all values and sub ranges in between. The appropriate refractory time window T_(r) can be pre-determined and/or pre-defined in one embodiment or, in an alternate embodiment, it can be selected by a user from within a certain pre-determined range. While inequality (1) was explicitly written for a monophasic hierarchical waveform, a similar inequality may be written for a biphasic waveform, or for a waveform that combines monophasic and biphasic elements.

A schematic illustration of ablation waveform delivery over multiple electrode sets j with a series of packets at the top level of the waveform hierarchy is provided in FIG. 8. The first waveform packet 632 is delivered over a sequence of j electrode sets in succession over the entire electrode sequence; the waveform parameters for this sequence satisfy a Diophantine inequality such as equation (1). This entire voltage waveform sequence is delivered within a defined refractory time window of a single paced heartbeat. After a packet delay t₃ equal to one pacing period, the next waveform packet 633 is delivered over the j electrode sets in succession over the entire electrode sequence with the same waveform parameters. The waveform delivery is continued over the pre-determined number of packets until the last waveform packet 636 is delivered over the j electrode sets in succession. Thus ablation delivery occurs over as many paced heartbeats as there are packets. The voltage amplitude for the waveform can range between approximately 700V and approximately 10,000V, and more preferably between approximately 1,000V and approximately 8,000V, as suitable and convenient for the clinical application, including all values and sub ranges in between.

In some embodiments, the complete sequence of electrode sets can be subdivided into smaller subsequences of electrode sets/electrode subsets. For example, the complete sequence of j electrode sets can be subdivided into N subsequences with j₁ electrode sets in the first subsequence/first subset, j₂ electrode sets in the second subsequence/second subset, and so on, with j_(N) electrode sets in the N-th subsequence. The waveform packets are applied first over the first subsequence of j₁ electrode sets, then over the second subsequence of j₂ electrode sets, and so on, with cardiac pacing employed throughout and all waveform packets applied within appropriate refractory time windows.

FIG. 9 is a schematic illustration of a system architecture for an ablation system 200 configured for delivery of pulsed voltage waveforms. The system 200 includes a system console 215, which in turn includes a pulsed waveform generator and controller 202, a user interface 203, and a switch 205 for isolating a connection box 210 (to which multiple catheters may be connected) from voltage pulses delivered by the generator. In some embodiments, the generator/controller 202 can include a processor, which can be any suitable processing device configured to run and/or execute a set of instructions or code. The processor can be, for example, a general purpose processor, a Field Programmable Gate Array (FPGA), an Application Specific Integrated Circuit (ASIC), a Digital Signal Processor (DSP), and/or the like. The processor can be configured to run and/or execute application processes and/or other modules, processes and/or functions associated with the system and/or a network associated therewith (not shown).

In some embodiments, the system 200 can also include a memory and/or a database (not shown) configured for, for example, storing pacing data, waveform information, and/or the like. The memory and/or the database can independently be, for example, a random access memory (RAM), a memory buffer, a hard drive, a database, an erasable programmable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), a read-only memory (ROM), Flash memory, and/or so forth. The memory and/or the database can store instructions to cause the generator/controller 202 to execute modules, processes and/or functions associated with the system 200, such as pulsed waveform generation and/or cardiac pacing.

The system 200 can be in communication with other devices (not shown) via, for example, one or more networks, each of which can be any type of network such as, for example, a local area network (LAN), a wide area network (WAN), a virtual network, a telecommunications network, and/or the Internet, implemented as a wired network and/or a wireless network. Any or all communications can be secured (e.g., encrypted) or unsecured, as is known in the art. The system 200 can include and/or encompass a personal computer, a server, a work station, a tablet, a mobile device, a cloud computing environment, an application or a module running on any of these platforms, and/or the like.

The system console 215 delivers ablation pulses to an ablation catheter 209 that is suitably positioned in a patient anatomy such as, for example, in a loop around the patient's pulmonary veins in a pericardial space of the patient's heart. An intracardiac ECG recording and pacing catheter 212 is coupled to an ECG recording system 208 via the connection box 210. The ECG recording system 208 is connected to a cardiac stimulator or pacing unit 207. The cardiac stimulator 207 can send a pacing output to the recording and pacing catheter 212; in general both atrial and ventricular pacing signals can be generated as outputs from the cardiac stimulator 207, and in some embodiments there can be separate intracardiac atrial and ventricular pacing catheters (not shown) or leads, each of which can then be disposed and/or positioned in the appropriate cardiac chamber. The same pacing output signal is also sent to the ablation system console 215. The pacing signal is received by the ablation system console and, based on the pacing signal, the ablation waveform can be generated by the generator/controller 202 within a common refractory window as described herein. In some embodiments, the common refractory window can start substantially immediately following the ventricular pacing signal (or after a very small delay) and last for a duration of approximately 130 ms or less thereafter. In this case, the entire ablation waveform packet is delivered within this duration, as explained earlier.

The user interface 203 associated with the ablation system console 215 can be implemented in a variety of forms as convenient for the application. When an epicardial ablation catheter is delivered via a subxiphoid approach and is placed epicardially around the pulmonary veins as shown in FIG. 1, it may be cinched in place at the ends 8 and 9 by passing the ends through a cinch tool. Depending on the size of the specific left atrial anatomy, a subset of the electrodes may be disposed around the pulmonary veins in encircling fashion while a remainder of the electrodes may be pulled inside the cinch tool (not shown in FIG. 1) and thus are not exposed. In such embodiments, the encircling/exposed electrodes can be selectively used for delivering ablation energy. An embodiment of a user interface suitable for use with an ablation catheter is schematically depicted in FIG. 10. In FIG. 10, a user selects the number of proximal electrodes inside the cinch tool and the number of distal electrodes inside the cinch tool as indicated in windows 653 and 654 respectively where the user has made selections 650 and 651 respectively for the respective numbers of electrodes. The complementary electrodes/subset of electrodes on the catheter (taken from the full set of catheter electrodes) that are not inside the cinch tool are the exposed electrodes to be used in the delivery of pulsed electric fields for electroporation ablation. The amplitude of the waveform to be delivered is controlled by an input mechanism such as, for example, the slider 658 that can be moved over a pre-determined voltage range indicated by 657 in FIG. 10. Once a voltage amplitude has been selected, an initialization (or Initialize) button 655 provided on the user interface is engaged to ready the ablation system for energy delivery. In one example, this can take the form of a trigger for charging a capacitor bank to store energy for subsequent delivery to the catheter.

As shown in FIG. 11, the Initialize button 660 can also act as a status indicator that indicates that the initialization process is ongoing. The status can be indicated by text (“Initializing . . . ” as shown in FIG. 11, and/or color, such as yellow to indicate that initialization has not yet started or is still in progress). Once the initialization process is complete (e.g., a capacitor bank is fully or satisfactorily charged), as shown in FIG. 12, the same button 663 now indicates completion of the process (“Initialized”) and, in some embodiments as illustrated, it can change color (e.g. change from yellow to green) and/or shape to further indicate completion of initialization. Meanwhile, the ablation system awaits reception of a pacing signal from a cardiac stimulator or pacing unit. Once a pacing signal is detected and/or confirmed together with completion of the initialization process, a second button 665 now becomes available for a user to engage, for confirmation of pacing capture. If a pacing signal is not detected by the ablation system console, then the second button 665 is not enabled. The user can monitor an ECG display (not shown) to view the cardiac stimulator pacing output in conjunction with intracardiac ECG recordings in order to confirm pacing capture (this confirms that atrial and ventricular contractions are indeed driven by the pacing signal, in order to establish a predictable common refractory window). Once the user visually confirms pacing capture from the ECG data, (s)he can then engage the “Confirm Pacing Capture” button 665 to confirm pacing capture on the ablation system.

As shown in FIG. 13, once pacing capture is confirmed on the ablation system, the system is now available for ablation or pulsed electric field delivery. The pacing capture confirmation button now changes appearance 670 (the appearance can change in color, shape, and/or the like) and indicates readiness for ablation delivery as shown by 670. Furthermore, an ablation delivery button 675 now becomes available to the user. The user can engage the ablation delivery button 675 to deliver ablation in synchrony with the paced heart rhythm. In some embodiments, the user engages the button 675 for the duration of ablation delivery, at the end of which the button changes shape or color to indicate completion of ablation delivery. In some embodiments, if the user disengages from the button 675 before ablation delivery is completed, ablation delivery is immediately stopped with only a small time lag of no more than, for example, 20 ms. In some embodiments, if the user has not engaged the ablation button 675 after it is displayed as being available, it stays available for engagement for only a limited time duration before it is disabled, as a safety mechanism. In some embodiments the ablation button 675 can be a software or graphic button on a user interface display, while in another embodiment it could be a mechanical button whose response depends on its state of activation or availability as determined by the system, or in another embodiment, the button 675 can be without limitation in the form of any of a variety of control input devices such as a lever, joystick, computer mouse, and so on. In one embodiment, the ablation system can have a separate emergency-stop button for additional safety, for example if it is desired to instantly de-activate the system. In one embodiment, the ablation console can be mounted on a rolling trolley or wheeled cart, and the user can control the system using a touchscreen interface that is in the sterile field. The touchscreen can be for example an LCD touchscreen in a plastic housing mountable to a standard medical rail or post and the touchscreen can have at a minimum the functionality described in the foregoing. The interface can for example be covered with a clear sterile plastic drape.

The waveform parameters as detailed herein can be determined by the design of the signal generator, and in some embodiments the parameters can be pre-determined. In some embodiments, at least a subset of the waveform parameters could be determined by user control as may be convenient for a given clinical application. The specific examples and descriptions herein are exemplary in nature and variations can be developed by those skilled in the art based on the material taught herein without departing from the scope of embodiments disclosed herein.

One or more embodiments described herein relate to a computer storage product with a non-transitory computer-readable medium (also can be referred to as a non-transitory processor-readable medium) having instructions or computer code thereon for performing various computer-implemented operations. The computer-readable medium (or processor-readable medium) is non-transitory in the sense that it does not include transitory propagating signals per se (e.g., a propagating electromagnetic wave carrying information on a transmission medium such as space or a cable). The media and computer code (also can be referred to as code or algorithm) may be those designed and constructed for the specific purpose or purposes. Examples of non-transitory computer-readable media include, but are not limited to, magnetic storage media such as hard disks, floppy disks, and magnetic tape; optical storage media such as Compact Disc/Digital Video Discs (CD/DVDs), Compact Disc-Read Only Memories (CD-ROMs), and holographic devices; magneto-optical storage media such as optical disks; carrier wave signal processing modules; and hardware devices that are specially configured to store and execute program code, such as Application-Specific Integrated Circuits (ASICs), Programmable Logic Devices (PLDs), Read-Only Memory (ROM) and Random-Access Memory (RAM) devices. Other embodiments described herein relate to a computer program product, which can include, for example, the instructions and/or computer code disclosed herein.

One or more embodiments and/or methods described herein can be performed by software (executed on hardware), hardware, or a combination thereof. Hardware modules may include, for example, a general-purpose processor (or microprocessor or microcontroller), a field programmable gate array (FPGA), and/or an application specific integrated circuit (ASIC). Software modules (executed on hardware) can be expressed in a variety of software languages (e.g., computer code), including C, C++, Java®, Ruby, Visual Basic®, and/or other object-oriented, procedural, or other programming language and development tools. Examples of computer code include, but are not limited to, micro-code or micro-instructions, machine instructions, such as produced by a compiler, code used to produce a web service, and files containing higher-level instructions that are executed by a computer using an interpreter. Additional examples of computer code include, but are not limited to, control signals, encrypted code, and compressed code.

While various embodiments have been described above, it should be understood that they have been presented by way of example, and not limitation. Where methods described above indicate certain events occurring in certain order, the ordering of certain events can be modified. Additionally, certain of the events may be performed concurrently in a parallel process when possible, as well as performed sequentially as described above 

What is claimed is:
 1. A system, comprising: a pulse waveform generator operatively coupled to an ablation device, the pulse waveform generator configured to: select electrode sets from a plurality of electrodes of the ablation device, each electrode set including a first subset of electrodes configured as one or more anodes and a second subset of electrodes configured as one or more cathodes; generate voltage pulses in the form of pulsed waveforms, each pulsed waveform including: (a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses; (b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and (c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and apply the voltage pulses to the electrode sets according to a predefined sequence with at least one pulsed waveform being applied across the first and second subsets of electrodes of each electrode set.
 2. The system of claim 1, wherein the pulse waveform generator is configured to apply the voltage pulses to the electrode sets by applying the pulsed waveforms to successive electrode sets within the predefined sequence offset by a fourth time delay.
 3. The system of claim 2, wherein the fourth time delay is at most about 5 milliseconds.
 4. The system of claim 2, wherein the pulse waveform generator is configured to generate and apply the voltage pulses such that a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of the electrode sets within the predefined sequence, the first time delay, the second time delay, and the fourth time delay are jointly constrained by a Diophantine inequality.
 5. The system of claim 1, wherein the plurality of electrodes is 4 electrodes.
 6. The system of claim 1, wherein the pulse waveform generator is configured to apply the voltage pulses to the electrode sets during refractory periods of cardiac cycles of a heart.
 7. The system of claim 1, wherein each pulse of the first set of pulses is a biphasic pulse with a voltage amplitude of at least 500 Volts and a pulse time duration being in the range from about 0.5 nanosecond to about 20 microseconds.
 8. The system of claim 1, wherein the first time delay is greater than a pulse time duration of each pulse of the first set of pulses.
 9. The system of claim 1, further comprising a cardiac stimulator configured to generate pacing signals for cardiac stimulation of a heart, the pulse waveform generator further operatively coupled to the cardiac stimulator and configured to apply the voltage pulses to the plurality of electrodes in synchrony with the pacing signals.
 10. A system, comprising: a pulse waveform generator operatively coupled to an ablation device, the pulse waveform generator configured to: receive a set of parameters for a pulsed waveform; generate voltage pulses in the form of pulsed waveforms according to the set of parameters, each pulsed waveform including: (a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses; (b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and (c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and apply the voltage pulses to an ablation device operatively coupled to the pulse waveform generator.
 11. The system of claim 10, wherein the pulse waveform generator is configured to apply the voltage pulses to the ablation device by applying the pulse waveforms over a sequence of electrode sets and with a fourth time delay offsetting application of the pulsed waveforms to successive electrode sets in the sequence.
 12. The system of claim 11, wherein the set of parameters is a first subset of parameters, the pulse waveform generator further configured to: determine a second subset of parameters for the pulsed waveform such that the first and second subsets of parameters collectively satisfy a Diophantine inequality.
 13. The system of claim 12, wherein the first and second subsets of parameters collectively include: a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of electrode sets within the sequence, the first time delay, the second time delay, and the fourth time delay.
 14. The system of claim 13, wherein the Diophantine inequality is j[m₂(m₁w+t₁(m₁−1))+t₂(m₂−1)]+t_(d)(j−1)<T_(r), where j is the number of electrode sets within the sequence, m₁ is the number of pulses in each first set of pulses, m₂ is the number first sets of pulses in the plurality of first set of pulses of each second set of pulses, t₁ is the first time delay, t₂ is the second time delay, t_(d) is the fourth time delay, w is a pulse width of each pulse in each first set of pulses, and T_(r) is a time period of a refractory period of a cardiac cycle.
 15. The system of claim 12, wherein the pulse waveform generator is configured to determine the second subset of parameters by: identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality; presenting the plurality of second subsets to a user; and receiving a selection indicative of the second subset from the plurality of second subsets to be used to generate the voltage pulses.
 16. The system of claim 12, wherein the pulse waveform generator is configured to determine the second subset of parameters by: identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality; and selecting the second subset from the plurality of second subsets to be used to generate the voltage pulses based on a predefined criterion.
 17. The system of claim 10, wherein each pulse of the first set of pulses is a biphasic pulse with a voltage amplitude of at least 500 Volts and a pulse time duration being in the range from about 0.5 nanosecond to about 20 microseconds.
 18. The system of claim 10, wherein the first time delay is greater than a pulse time duration of each pulse of the first set of pulses.
 19. A method, comprising: selecting electrode sets from a plurality of electrodes of an ablation device, each electrode set including a first subset of electrodes configured to be anodes and a second subset of electrodes configured to be cathodes; generating voltage pulses in the form of pulsed waveforms, each pulsed waveform including: (a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses; (b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and (c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and applying the voltage pulses to the electrode sets according to a predefined sequence with at least one pulsed waveform being applied across the first and second subsets of electrodes of each electrode set.
 20. The method of claim 19, wherein applying the voltage pulses to the electrode sets includes applying the pulsed waveforms to successive electrode sets within the predefined sequence offset by a fourth time delay.
 21. The method of claim 20, wherein a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of the electrode sets within the predefined sequence, the first time delay, the second time delay, and the fourth time delay are jointly constrained by a Diophantine inequality.
 22. The method of claim 19, wherein applying the voltage pulses to the electrode sets is during refractory periods of cardiac cycles of a heart.
 23. The method of claim 19, wherein applying the voltage pulses to the electrode sets is in synchrony with pacing signals generated by a cardiac stimulator.
 24. A method, comprising: receiving a set of parameters for a pulsed waveform; generating voltage pulses in the form of pulsed waveforms according to the set of parameters, each pulsed waveform including: (a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses; (b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and (c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and applying the voltage pulses to an ablation device.
 25. The method of claim 24, wherein applying the voltage pulses to the ablation device includes applying the pulse waveforms over a sequence of electrode sets and with a fourth time delay offsetting application of the pulsed waveforms to successive electrode sets in the sequence.
 26. The method of claim 24, wherein the set of parameters is a first subset of parameters, the method further comprising determining a second subset of parameters for the pulsed waveform such that the first and second subsets of parameters collectively satisfy a Diophantine inequality.
 27. The method of claim 26, wherein the first and second subsets of parameters collectively include: a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of electrode sets within the sequence, the first time delay, the second time delay, and the fourth time delay.
 28. The method of claim 27, wherein the Diophantine inequality is j[m₂(m₁w+t₁(m₁−1))+t₂(m₂−1)]+t_(d)(j−1)<T_(r), where j is the number of electrode sets within the sequence, m₁ is the number of pulses in each first set of pulses, m₂ is the number first sets of pulses in the plurality of first set of pulses of each second set of pulses, t₁ is the first time delay, t₂ is the second time delay, t_(d) is the fourth time delay, w is a pulse width of each pulse in each first set of pulses, and T_(r) is a time period of a refractory period of a cardiac cycle.
 29. The method of claim 26, wherein determining the second subset of parameters includes: identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality; presenting the plurality of second subsets to a user; and receiving a selection indicative of the second subset from the plurality of second subsets to be used to generate the voltage pulses.
 30. The method of claim 26, wherein determining the second subset of parameters includes: identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality; and selecting the second subset from the plurality of second subsets to be used to generate the voltage pulses based on a predefined criterion. 